engleski

AdS-inspired noncommutative gravity on the Moyal plane

We consider noncommutative gravity on a space with canonical noncommutativity that is based on the commutative MacDowell-Mansouri action. Gravity is treated as gauge theory of the noncommutative SOð1 ; 3Þ? group, and the Seiberg-Witten map is used to express noncommutative fields in terms of the corresponding commutative fields. In the commutative limit the noncommutative action reduces to the Einstein-Hilbert action plus the cosmological term and the topological Gauss-Bonnet term. After the Seiberg-Witten expansion in the noncommutative parameter the first order correction to the action, as expected, vanishes. We calculate the second order correction and write it in a manifestly gauge covariant way.

noncommutative geometry ; gravity ; Anti de Sitter

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